This M.S. thesis introduces new modulus scaling techniques for transforming a class of primes into special forms which enable efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of a scaled modulus. Our inversion algorithm exhibits superior performance to the Euc...

Field inversion in F2m dominates the cost of modern software implementations of certain elliptic curve cryptographic operations, such as point encoding/hashing into elliptic curves. [7, 6, 2] Itoh–Tsujii inversion using a polynomial basis and precomputed table-based multi-squaring has been demonstrated to be highly effective for software implementations [19, 14, 2], but the performance and memo...

Given a faithful parameterization P(t) of a rational plane curve, an inversion formula t = f(x,y) gives the parameter value corresponding to a point (x,y) on the curve, where f is a rational function in x and y. We investigate the relationship between a point (x*, y*) not on the curve and the corresponding point P(t*) on the curve, where t* = f(x*, y*). It is shown that for a rational quadratic...

In the underlying finite field arithmetic of an elliptic curve cryptosystem, field multiplication is the next computational costly operation other than field inversion. We present two novel algorithms for efficient implementation of field multiplication and modular reduction used frequently in an elliptic curve cryptosystem defined over GF (2). We provide a complexity study of the two algorithm...

Unshifted and shifted multiscaling functions are used as mathematical models for curve fitting of irregularly sampled data. This pre-processing procedure combined with multiwavelet neural networks for data-adaptive curve fitting is shown to perform well in the case of high resolution. In the case of low resolution it is more accurate than numerical integration and cheaper than matrix inversion....

The hyperelliptic curve Ate pairing provides an efficient way to compute a bilinear pairing on the Jacobian variety of a hyperelliptic curve. We prove that, for supersingular elliptic curves with embedding degree two, square of the Ate pairing is nothing but the Weil pairing. Using the formula, we develop an X -coordinate only pairing inversion method. However, the algorithm is still infeasible...

Multiwavelets are briefly reviewed and preprocessing and postprocessing for such wavelets are introduced. Least squares curve fitting of irregularly sampled data is achieved by means of unshifted and shifted multiscaling functions. This preprocessing procedure combined with multiwavelet neural networks for data-adaptive curve fitting is shown to perform well in the case of high resolution. In t...

This paper presents a method to determine the shape of a space object while simultaneously recovering the observed space object’s inertial orientation. This paper employs an Adaptive Hamiltonian Markov Chain Monte Carlo estimation approach, which uses light curve data to infer the space object’s orientation, shape, and surface parameters. This method is shown to work well for relatively high di...

Ground-penetrating radar (GPR) data affected by waveguide dispersion are not straightforward to analyse. Therefore, waveguide dispersed common midpoint measurements are typically interpreted using so-called dispersion curves, which describe the phase velocity as a function of frequency. These dispersion curves are typically evaluated with deterministic optimization algorithms that derive the di...

A novel control scheme, fuzzy immune adaptive model inversion control, was put forward, aiming at the large flight envelope curve control problem of helicopter. The proposed scheme was designed based on model inversion theory, biology immune response mechanism and fuzzy control method. It could achieve effective control throughout large flight envelope curve via the design of fuzzy immune onlin...